These are some practice problems that I have and I need help solving so that I can get back to solving the actual problems I need to do$.$ I just need a detailed explanation on how each problem was solved and hopefully use that info in my actual assignment.

Problem $12\mathrm{.}2$: Compute the Volume of a Solid Obtained from Revolving about the $y-$axis.

Suppose the region $($in Quadrant I$)$ bounded by the function $f(x)=e^x,$ the $y-$axis, and the line $y=5$ is revolved about the $y-$axis.

Write $($but do not evaluate$)$ a definite integral to represent the volume of the resulting solid of revolution.

Problem $12\mathrm{.}3$: Compute the Volume of a Solid Obtained from Revolving about a Horizontal Line

Suppose the region bounded by the function $f(x)=e^x,$ the $y-$axis, and the line $y=5$ is revolved about the line $y=5.$

Write $($but do not evaluate$)$ a definite integral to represent the volume of the resulting solid of revolution.

Problem $12\mathrm{.}4$: Compute the Volume of a Solid Obtained from Revolving about a Vertical Line

Suppose the region bounded by the function $f(y)=\frac{3}{y}$ and the lines $x=2$ and $y=6$ is revolved about the line $x=2$

$($a$)$ Write a definite integral to represent the volume of the resulting solid of revolution.

$($b$)$ Evaluate the definite integral. Show your work.